1

Rose chooses R1 every time. Colin chooses C2 or C2.

The game equilibrium equals 10. However, it is not a pure strategy Nash Equilibrium since Colin can choose either C2 or C3 and get the same result.

2

Pitcher chooses knuckleball every time, it is a dominant strategy. The Batter must subsequently guess knuckleball each time.

The pure strategy Nash equilibrium equals 0.250.

3

Linear Program for Rose Linear Program for Rose

Linear Program for Colin Linear Program for Colin

4

library(lpSolve)
payoff.matrix <- as.matrix(rbind(
  c(3000, 4500, 6000),
  c(1000, 9000, 2000),
  c(4500, 4000, 3500)))

5

Maximin = 20, Minimax = 15, therefore no pure strategy staddle point exists.

Colin plays C1 or C2 Rose plays R1 Game value: 10

6

  1. equating expected value

First, check for pure strategy saddle point:
check for pure strategy saddle point
One exists at C1, R2 and equals 0.6.

  1. methods of oddments

This method cannot be used due to the saddle point.

7

If both players maximize strategy, the likely outcome is (2,4).

8

The most likely outcome is for both players to try from long range on their first shot, with an expected value of -2 for Doc Holiday since he’s the worse long-range shot.